Question

Solve the following problems.1. Given <1 and <2 are a linear pair. 22 and 23 are a linear pair. Prove: 21€ 23.2. Given: 1 || m. Write a flowchart proof to show that Z1 Z3.

Answer 1

Recall that two angles are a linear pair if they add up to 180 degrees, therefore:

$\begin{gathered} \measuredangle1+\measuredangle2=180^{\circ}, \\ \measuredangle2+\measuredangle3=180^{\circ}. \end{gathered}$

Then,

$\measuredangle1+\measuredangle2=\measuredangle2+\measuredangle3.$

Subtracting ∡2 from the above equation we get:

$\begin{gathered} \measuredangle1+\measuredangle2-\measuredangle2=\measuredangle2+\measuredangle3-\measuredangle2, \\ \measuredangle1=\measuredangle3. \end{gathered}$

Therefore

$\measuredangle1\cong\measuredangle3.$